Appendix; The Callendar - Van Dusen Method - Endress+Hauser iTEMP HART TMT162 Bedienungsanleitung

TMT162
Endress+Hauser
11

Appendix

11.1

The Callendar - van Dusen Method

It is a method to match sensor and transmitter to improve the accuracy of the measurement system.
According to IEC 60751, the non-linearity of the platinum thermometer can be expressed as (1):
R
T
in which C is only applicable when T < 0 °C.
The coefficients A, B, and C for a standard sensor are stated in IEC 60751. If a standard sensor is
not available or if a greater accuracy is required than can be obtained from the coefficients in the
standard, the coefficients can be measured individually for each sensor. This can be done e.g. by
determining the resistance value at a number of known temperatures and then determining the
coefficients A, B, and C by regression analysis.
However, an alternative method for determination of these coefficients exists. This method is based
on the measuring of 4 known temperatures:
• Measure R at T = 0 °C (the freezing point of water)
0 0
• Measure R at T = 100 °C (the boiling point of water)
100 100
• Measure R at T = a high temperature (e.g. the freezing point of zink, 419.53 °C)
h h
• Measure R at T = a low temperature (e.g. the boiling point of oxygen, -182.96 °C)
l l
Calculation of α
First the linear parameter α is determined as the normalized slope between 0 and 100 °C (2):
If this rough approximation is enough, the resistance at other temperatures can be calculated as (3):
and the temperature as a function of the resistance value as (4):
Calculation of δ
Callendar has established a better approximation by introducing a term of the second order, δ , into
the function. The calculation of δ is based on the disparity between the actual temperature, T
the temperature calculated in (4) (5):
With the introduction of δ into the equation, the resistance value for positive temperatures can be
calculated with great accuracy (6):
R
T
Calculation of β
At negative temperatures (6) will still give a small deviation. Van Dusen therefore introduced a term
of the fourth order, β , which is only applicable for T < 0 °C. The calculation of β is based on the
2
= R [ 1 AT BT + + +
0
R –
-------------------- - 100
a =
100 R ·
R = R + R
T 0
0
R – R
------------------- -
T =
T
R ·
0
RT
h
---------------------- -
T –
h
R
------------------------------------- - 0
d =
ö T
T
æ æ
-------- - 1 h
–
è ø è
100
æ
-------- - 1
= R + R a T ( + – d
0
0 è
100
3
C T 100 ( – )T ]
R
0
0
a T ·
0
a
– R
0
· a
ö
h
-------- -
ø
100
T
T
ö æ ö ö
-------- -
–
ø è ø ø
100
Appendix
, and
h
101